2017
DOI: 10.1186/s13660-017-1418-8
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Stochastic inequalities and applications to dynamics analysis of a novel SIVS epidemic model with jumps

Abstract: This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the resu… Show more

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Cited by 67 publications
(26 citation statements)
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“…The procedure goes like this: when the number of species reaches a specific requirement, the harvesting strategy is implemented, otherwise the harvesting behavior is suppressed. Some other related studies can be found in [34][35][36][37][38][39] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…The procedure goes like this: when the number of species reaches a specific requirement, the harvesting strategy is implemented, otherwise the harvesting behavior is suppressed. Some other related studies can be found in [34][35][36][37][38][39] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…More mathematical models about microorganism cultivation with constant dilution rate and perturbed phenomena could be found in [17][18][19][20][21][22][23][24]. The study of stochastic population models has been a focus of some scholars in recent years (see [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]). …”
Section: Introductionmentioning
confidence: 99%
“…Zou et al [26] considered a population dynamic system with the delays and impulses and obtained sufficient conditions for the coexistence of two populations. For more applications of differential equations, see [27][28][29][30][31][32][33][34][35][36][37][38].…”
Section: Introductionmentioning
confidence: 99%